ST. LOUIS -- David Price arrived into town Sunday night, walked across the street, caught the St. Louis Cardinals' game, drank a couple of beers, and had a nice, leisurely lunch the next day.

And never had to pay for a thing.

Price, who arrived in the seventh inning with 10 of his buddies, was even offered a suite. He politely declined, and plopped in the third row of the second deck, right in Big Mac Land, cheering like any other fan at Busch Stadium.

It was that way everywhere he went these past two days. Folks welcomed him to town. And then begged him to stay.

Price is scheduled to leave town on a chartered plane Wednesday night with the rest of his Tampa Bay Rays teammates, but Cardinals fans are making sure to let him know he's welcome to stay a while longer.

Like, for the next 1 ½ years, if not the rest of his working career.

"The people here have been great,'' said Price, the Rays ace who lives about a five-hour drive away in Nashville. "They're awesome. I couldn't have been treated any nicer.''

The St. Louis Cardinals are doing everything but bring room service to Price during his stay.

OK, well maybe not the Cardinals themselves, but they're letting their fans and stadium workers handle the sales pitch.

The Cardinals want Price. They need Price. And if he happens to be traded to the Cardinals, and is willing to sign a long-term contract, well, they'd be happy to name an Italian restaurant on The Hill in his honor.

Yes, Price is that big, that important, and is the only player on the trade market who can make the difference between a contender and a World Series championship.

If the Rays decide to trade Price, and that decision hinges on how they fare in the next week, he's likely going to the Cardinals, Los Angeles Dodgers or Seattle Mariners.

Yet, one-high ranking American League club executive predicts that if the Rays trade Price, one team stands out from the rest.

Yes, St. Louis.

Price, 28, certainly has his preferences if he's forced to leave Tampa, but reminds you that he has no say. He has no trade provisions in his contract. His only leverage is that he can decide whether to negotiate a long-term contract once he's traded, or wait until free agency after the 2015 season.

The Cardinals would prefer to take their chances right now. They've got the prized pieces to at least entice the Rays. You want prized outfielder Oscar Taveras? You got him. Starting pitcher Shelby Miller? Done. More prospects? Go ahead and name them.

"Who wouldn't want him?'' Dodgers starter Dan Haren says. "He would be would be nice for anyone to have. Any team that gets him would be lucky to have him."

When you are the most dominant pitcher in the American League these days, the contender that acquires Price may as well start planning that parade route, because a World Series could be coming your way.

Let's see, the dude is 4-0 with a 0.87 ERA in July, and has won five consecutive starts. He has pitched at least eight innings in eight of his last 11 starts. He hasn't given up a run in his last 16 innings. And, oh yeah, he has struck out a major-league leading 173 hitters.

"I've never seen him pitch any better,'' says Rays catcher Jose Molina, 39, who the Cardinals also would love to acquire until his younger brother, Yadier, returns from his torn thumb ligament. "He's doing everything he wants to on the mound. He's in complete control.''

Well, except of his own fate.

The Rays, who had baseball's worst record just five weeks ago, suddenly are playing better than anyone in the major leagues, winning 23 of their last 34 games, and climbing to within eight games of the Baltimore Orioles.

Considering the mediocrity in the AL East, the Rays might be stupid to give up, knowing they can actually win this thing.

"Are we trying to win here? What we going to do?'' Rays veteran reliever Grant Balfour said. "If you want to give us a chance to win, we keep him. This is a six-month season. Why would you want to give up after four months?''

Yet these are the Rays. They play in a dump. They can't draw fans. And they can't afford to keep their own star players.

They may be able to keep Price now, but certainly not after this winter, when his salary is expected to hit $20 million in salary arbitration.

If the Rays' front office doesn't believe they can win now, why not shop Price, and see if they're tempted to move him?

"You don't want to see guys get traded, but you understand why,'' Rays starter Alex Cobb says. "I've seen how the organization has been run since I've been here, seen the way they operated. So I would absolutely understand it.

"I'm not going to say I wouldn't be upset for a while, but in the long run, I know they would do what they think is the best fit for us.''

The Rays are careful not to broach the subject with Price. Price certainly doesn't want to hear it. He tries to stay away from the rumors. The only time he knows his name is floated to a team is if a new fan base is suddenly joining his 221,000-strong Twitter following.

"I don't want to let anyone with my situation affect how I am in the clubhouse and on the field,'' Price said. "If I let it affect me, then it'll definitely affect the team, and affect my teammates. I don't want to be a distraction.''

Price, who last attended a game as a fan was when he was about 14, watching Mark McGwire launch home run balls at old Busch Stadium, realizes he has to be careful, too. He talked last week about how cool it would be to part of a Chicago Cubs team that won their first World Series since 1908.

The next thing he knew, folks thought he was campaigning to join them.

"I still stand behind that,'' Price said. "I think everybody in baseball would say that if you won a championship in Chicago, you would have statues. You would have restaurants. People would name their kids after you. That's a part of history. Everybody wants to be part of history. …

"It doesn't mean that I want to play there.''

Then again, there are plenty of statues in front of Busch Stadium, and restaurants owned by Cardinals players and broadcasters, that make winning in St. Louis pretty cool, too.

"I did get a free meal (Monday),'' Price said. "So that was pretty awesome.''

It may be just the beginning. ​

GALLERY: TRADE DEADLINE TRACKER

July 31: The Rays traded LHP David Price to the Tigers in a three-team trade with the Mariners. The Mariners received OF Austin Jackson; the Rays got LHP Drew Smyly, INF Nick Franklin and minor league INF Willy Adames. Jesse Johnson, USA TODAY Sports